Russian Defence Minister Sergei Shoigu has promised a "harsh response" to cross-border incursions from Ukraine.
His comments came after Moscow said it had defeated an attack in the Belgorod region.
However, regional governor Vyacheslav Gladkov said there had been a "large number" of drone attacks overnight.
Ukraine denies involvement in the raid - and two Russian paramilitary groups opposed to Russian President Vladimir Putin say they were behind it.